Provision of image data

ABSTRACT

A method and apparatus are disclosed for providing image data. The method includes the steps of providing incident radiation from a radiation source at a target object and, via at least one detector, detecting an intensity of radiation scattered by the target object. Also via the at least one detector an intensity of radiation provided by the radiation source absent the target object is detected. Image data is provided via an iterative process responsive to the intensity of radiation detected absent the target object and the detected intensity of radiation scattered by the target object.

The present invention relates to a method and apparatus for providingimage data of the type which may be utilised to construct an image of aregion of a target object. In particular, but not exclusively, thepresent invention relates to a method of providing such image data usingan iterative process making use of an unknown probe function.

Many types of imaging techniques are known for deriving spatialinformation about a target object (sometimes referred to as a specimen).For example in conventional transmission imaging an object is irradiatedby plane wave illumination. The waves scattered by the object arere-interfered by a lens to form an image. In the case of very short wavelength imaging (X-rays or electrons) this technique has many knowndifficulties associated with aberrations and instabilities introduced bythe lens which limit the resolution and interpretability of theresulting image. Typical achievable resolution is many times larger thanthe theoretical limit. Other types of imaging techniques are known butmany of these have problems such as resolution limits, long datagathering times or the need for complex and expensive equipment.

A technique for high resolution imaging has been disclosed in WO2005/106531. This document, which is herein incorporated by referencefor all purposes, discloses a method and apparatus of providing imagedata for constructing an image of a region of a target object whichincludes the steps of providing incident radiation from a radiationsource at a target object. Via at least one detector, detecting theintensity of radiation scattered by the target object and providingimage data responsive to the detected intensity without high resolutionpositioning of the incident radiation or a post target object aperturerelative to the target object. Also disclosed is a method for providingsuch image data via an iterative process using a moveable softly varyingprobe function such as a transmittance function or illuminationfunction.

Those skilled in the art now refer to the technique disclosed in WO2005/106531 as the ptychographical iterative engine (or PIE). This is apowerful technique for the recovery of image data relating to an area ofan object from a set of diffraction pattern measurements. Eachdiffraction pattern is formed by illuminating an object with a knownwave front of coherent radiation with the requirement that the intensityof the wave front is concentrated within a localised lateral regionwhere it interacts with the object. Examples of such a wave front wouldbe that generated a short distance beyond an aperture when it isilluminated by a plane wave, or the focal spot generated by a convexlens illuminated by a plane wave. The technique is also applicable toscenarios where a target is illuminated by plane wave radiation and apost target object aperture is used to select illumination scattered bya region of the object.

In this sense a diffraction pattern is the distribution of intensityproduced by an optical configuration some distance beyond the object andat a plane normal to the direction of propagation of the illuminationwave front. This plane is designated as the measurement plane andmeasurements made at this plane are denoted Ψ_(k) (u) with u being anappropriate coordinate vector. It is to be noted that when the distancebetween the measurement plane and a sample plane is small thediffraction pattern is known as a near-field diffraction pattern. Whenthis distance is large the diffraction pattern is known as a far-fielddiffraction pattern.

Ptychography relies upon the recording of several diffraction patternsat the measurement plane using a suitable recording device such as a CCDcamera or the like. The lateral positions of the object and thelocalised illumination wave front are different for each pattern.

In order to provide useful image data characteristics of a probefunction which might be a transmittance function associated with a posttarget object aperture or an illumination function associated withincident radiation itself must be known or estimated. This eitherrequires time consuming set up techniques or can lead to inaccuracies ifthe probe function used is in accurate. Furthermore the iterativeprocess can be time consuming.

It is an aim of the present invention to at least partly mitigate theabove-mentioned problems.

It is an aim of certain embodiments of the present invention to providea method and apparatus suitable for providing image data which may ormay not be used to construct an image of a region of a target object andwhich can be utilised without careful knowledge of a probe functionbeing required.

It is an aim of certain embodiments of the present invention to providea method and apparatus for providing image data in which an iterativeprocess is used which produces useful results in an efficient manner.

According to a first aspect of the present invention there is provided amethod of providing image data for constructing an image of a region ofa target object, comprising the steps of:

-   -   providing incident radiation from a radiation source at a target        object and, via at least one detector, detecting an intensity of        radiation scattered by the target object;    -   via the at least one detector, detecting an intensity of        radiation provided by the radiation source absent the target        object; and    -   providing image data via an iterative process responsive to the        intensity of radiation detected absent the target object and the        detected intensity of radiation scattered by the target object.

According to a second aspect of the present invention there is providedapparatus for providing image data for generating an image of a regionof a target object, comprising:

-   -   locating means for locating a target object at a predetermined        location;    -   a radiation source for providing incident radiation at a target        object located by the locating means;    -   at least one detector device for detecting an intensity of        radiation scattered by the target object locating means for        locating incident radiation or a post-target aperture at one or        more locations with respect to the target object; and    -   processing means for providing image data via an iterative        process responsive to an intensity of radiation detected absent        the target object and a detected intensity of radiation        scattered by the target object.

Certain embodiments of the present invention provide the advantage thatduring an iterative process a probe function is itself iterativelycalculated step by step with a running estimate of the probe functionbeing utilised to determine running estimates of an object functionassociated with the target object.

Certain embodiments of the present invention provide the advantage thatillumination from an optical set up without a target may be efficientlymeasured before and/or after analysing a target object. This obviatesthe need for a probe function to be measured at other times.

Certain embodiments of the present invention provide a method ofproviding high resolution images using image data gathered via aniterative process and constructing an image therefrom.

Certain embodiments of the present invention provide the advantage thatimage data indicating characteristics of a target object may be providedwhich may then be processed as data so as to determine some othercharacteristic of a target object. As such an image is not necessarilyconstructed using the image data.

Embodiments of the present invention will now be described hereinafter,by way of example only, with reference to the accompanying drawings inwhich:

FIG. 1 illustrates incident at a target object;

FIG. 2 illustrates a Probe Function and formation of a diffractionpattern with a target object;

FIG. 3 illustrates a phase retrieval algorithm; and

FIG. 4 illustrates a Probe Function and formation of a diffractionpattern without a target object; and

FIG. 5 illustrates an apparatus for providing imaged data that may beused to construct a high resolution image according to embodiments ofthe FIGS. 1-2.

In the drawings like reference numerals refer to like parts.

FIG. 1 illustrates how a scattering pattern may be developed and used todetermine image data corresponding to information about the structure ofa target object. It will be understood that the term target objectrefers to any specimen or item placed in the path of incident radiationwhich causes scattering of that radiation. It will be understood thatthe target object should be at least partially transparent to incidentradiation. The target object may or may not have some repetitivestructure. Alternatively the target object may be wholly or partiallyreflective in which case a scattering pattern is measured based onreflected radiation.

Incident radiation 10 is caused to fall upon the target object 11. It isto be understood that the term radiation is to be broadly construed asenergy from a radiation source. This will include electro magneticradiation including X-rays, emitted particles such as electrons and/oracoustic waves. Such radiation may be represented by a wave functionΨ(r). This wave function includes a real part and an imaginary part aswill be understood by those skilled in the art. This may be representedby the wave functions modulus and phase. Ψ(r)* is the complex conjugateof Ψ(r) and Ψ(r) Ψ(r)*=|Ψ(r)|² where |Ψ(r)|² is an intensity which maybe measured for the wave function.

The incident radiation 10 is scattered as it passes through and beyondthe specimen 11. As such the wave function of the incident radiation asit exits the specimen will be modified in both amplitude and phase withrespect to the wave function of the incident radiation at the pre-targetside of the specimen. The scattering which occurs may include Fourierdiffraction, refraction and/or Fresnel diffraction and any other form ofscattering in which characteristics of the incident radiation aremodified as a result of propagating after the specimen. If an array ofdetectors such as a CCD detector 12 is arranged a long distance from thespecimen then a diffraction pattern is formed at a diffraction plane 13.A Fourier diffraction pattern will form if the detectors 12 are locateda distance D from the specimen where D is sufficiently long for thediffraction pattern to be formed effectively from a point source. If thediffraction plane is formed closer to the specimen, by locating thedetectors nearer, then a Fresnel diffraction pattern will be formed.

The incident radiation 10 falls upon a first surface of a target object11. The incident radiation is scattered in the specimen and transmittedradiation propagates through to a diffraction plane 13 where adiffraction pattern forms.

FIG. 2 illustrates the process of FIG. 1 in more detail. The radiation10 is roughly focused, for example by a weak lens, so that a region of afirst surface of the target object is illuminated. The weak lens may ofcourse comprise any appropriate focusing apparatus such as a set ofplates and a voltage supply for a beam of electrons or a reflectivesurface for X-rays. The weak focusing is sufficient to substantiallyconfine the probing radiation beam. It is thus not necessary to sharplyfocus radiation although of course strongly focussed radiation could beused. Here the target object provides an object function O(r) whichrepresents the phase and amplitude alteration introduced into anincident wave as a result of passing through the object of interest. Theilluminating radiation incident on the target object represents a probefunction P(r) which forms an illumination function such as thatgenerated by a caustic or illumination profile formed by the lens orother optical component. P(r) is the complex stationary value of thiswave field calculated at the plane of the object. The exit wave functionψ(r,R) defines the scattered radiation as it exits the downstreamsurface of the target object. As this exit wave propagates through spaceit will form a diffraction pattern Ψ(u) at the diffraction plane 13.

It will be understood that rather than weakly (or indeed strongly)focusing illumination on a target, unfocused radiation can be used witha post target aperture. An aperture is located post target object tothereby select a region of the target for investigation. The aperture isformed in a mask so that the aperture defines a “support”. A support isan area of a function where that function is not zero. In other wordsoutside the support the function is zero. Outside the support the maskblocks the transmittance of radiation. The term aperture describes alocalised transmission function of radiation. This may be represented bya complex variable in two dimensions having a modulus value between 0and 1. An example is a mask having a physical aperture region of varyingtransmittance.

Incident radiation would thus fall upon the up-stream side of thespecimen and be scattered by the specimen as it is transmitted. Aspecimen wave O(r) is thus formed as an exit wave function of radiationafter interaction with the object. In this way O(r) represents atwo-dimensional complex function so that each point in O(r), where r isa two-dimensional coordinate, has associated with it a complex number.O(r) will physically represent an exit wave that would emanate from theobject which is illuminated by a plane wave. For example, in the case ofelectron scattering, O(r) would represent the phase and amplitudealteration introduced into an incident wave as a result of passingthrough the object of interest. The aperture provides a probe functionP(r) (or transmission function) which selects a part of the object exitwave function for analysis. It will be understood that rather thanselecting an aperture a transmission grating or other such filteringfunction may be located downstream of the object function. The probefunction P(r−R) is an aperture transmission function where an apertureis at a position R. The probe function can be represented as a complexfunction with its complex value given by a modulus and phase whichrepresent the modulus and phase alterations introduced by the probe intoa perfect plane wave incident up it.

The exit wave function ψ(r,R) is an exit wave function of radiation asit exits the aperture. This exit wave ψ(r,R) forms a diffraction patternΨ(u) at a diffraction plane. Here r is a vector coordinate in real spaceand u is a vector coordinate in diffraction space.

It will be understood that with both the aperture formed embodiment andthe non-aperture embodiment described with respect to FIGS. 1 and 2 ifthe diffraction plane at which scattered radiation is detected is movednearer to the specimen then Fresnel diffraction patterns will bedetected rather than Fourier diffraction patterns. In such a case thepropagation function from the exit wave ψ(r,R) to the diffractionpattern Ψ(u) will be a Fresnel transform rather than a Fouriertransform.

FIG. 3 illustrates an iterative process according to an embodiment ofthe present invention which can be used to recover image data of thetype which can be used to construct an image of an area of an objectfrom a set of diffraction patterns. The iterative process 30 illustratedbegins with a guess 31 at the object and a guess 32 at the form of aprobe function used. Subsequently these initial guesses are replaced byrunning guesses in the iterative process. The initial guesses for theimage and/or probe function can be random distributions or canthemselves be precalculated approximations based on other measurementsor prior calculations. The guesses are modelled at a number of samplepoints and are thus represented by matrices. Such matrices can be storedand manipulated by a computer or other such processing unit. Aptly thesample points are equally spaced and form a rectangular array. The probefunction estimation after k iterations is denoted by P_(k)(r) and therecovered image after k iterations by O_(k)(r). The original guesses forthe probe function and objection function are thus P₀(r) and O₀(r)respectively where r is an appropriate coordinate vector.

If the current translation vector relating to the relative positions ofthe object and the probe function is denoted R_(k) then the interactionbetween the guessed-at object distribution and the probe function ismodelled byψ_(k)(r,R _(k))=O _(k)(r)P _(k)(r−R _(k))  1

This is the current exit wave front. According to embodiments of thepresent invention an iterative process is used to update the objectguess. This is illustrated by the left hand box 33 in FIG. 3. An updatedprobe function guess is also iteratively calculated which is illustratedby the right hand box 34 in FIG. 3.

Referring to the update of the object guess a first step is to determinethe exit wave front ψ(r, R_(k)) at step 35. This is carried out usingequation 1 noted above. A next step is to propagate the exit wave frontto the measurement plane which is accomplished using a suitable model ofpropagation for the coherent wave front. The propagation is representedby the operator T where:Ψ_(k)(u)=

[ψ_(k)(r,R _(k))]  2

The forward transform T shown as step 36 generates a propagated wavefront Ψ_(k)(u) where u references coordinates in the measurement plane.Since Ψ_(k)(u) is complex-value this can be written as:Ψ_(k)(u)=A _(k)(u)exp(iθ _(k)(u))  3

Next this modelled wave front must be compared to a measured diffractionpattern. If the guessed-at object is correct then the following equalityholds for every value of k.A _(k)(u)=√{square root over (Ω_(k)(u))}  4

The modulus of the propagated exit wave front equals the square root ofthe recorded diffraction pattern intensity. Generally this will not bethe case as the guessed-at object will not correctly represent the trueobject at the sample points. To enforce the equality the modulus of thepropagated exit wave front is replaced by the square root of therecorded diffraction pattern intensity as:Ψ′_(k)(u)=√{square root over (Ω_(k)(u))}exp(iθ _(k)(u))  5

At step 37 the modulus of the propagated exit wave front is replaced bythe square root of the recorded diffraction pattern intensity.

The corrected wave front is then propagated back to the plane of theobject using the inverse propagation operator:ψ′_(k)(r,R _(k))=

⁻¹[Ψ′_(k)(u)]  6

This inverse propagation step 39 provides the corrected exit wave formψ′_(k)(r, R_(k)). An update step 40 is then calculated to produce animproved object guess O_(k+1)(r). The update step 40 is carried outaccording to:

$\begin{matrix}{{O_{k + 1}(r)} = {{O_{k}(r)} + {\alpha\frac{P_{k}^{*}\left( {r - R} \right)}{{{P_{k}\left( {r - R} \right)}}_{\max}^{2}}\left( {{\psi_{k}^{\prime}\left( {r,R} \right)} - {\psi_{k}\left( {r,R} \right)}} \right)}}} & 7\end{matrix}$

This update function is labelled U1 in FIG. 3 which generates the updateof the object guess O_(k+1)(r). The parameter α governs the rate ofchange of the object guess. This value should be adjusted between 0 and2 as higher values may lead to instability in the updated object guess.According to embodiments of the present invention the probe function isreconstructed in much the same manner as the object function. Aptly theprobe function guess is carried out concurrently with the update of theobject guess. (It will be appreciated that the Probe Function couldoptionally be updated more often or less often then the ObjectFunction). In order to achieve this a further diffraction pattern isrecorded in the measurement plane with the target object removed fromthe system. This further diffraction pattern may be recorded prior tothe target object being put in place or subsequent to removal of thetarget object after the previously mentioned diffraction patterns havebeen used or may be a combination of diffraction patterns recordedbefore and after the target object is duly located.

That is to say the diffraction pattern of the probe function itself isrecorded. This is denoted as the measurement Ω_(P)(u). The measurementof this diffraction pattern is illustrated in FIG. 4.

At step 32 P₀(r) is chosen as an initial guess at the probe functionwhich may be random or an approximation based on previous othermeasurements or calculations. Proceeding in a similar manner to thecorrection/update steps detailed above the probe function guess ispropagated with a transform to the measurement plane so that:Ψ_(k)(u)=

[P _(k)(r)]  8which can be written as:Ψ_(k)(u)=B _(k)(u)exp(iγ _(k)(u))  9

A correction step 43 is then implemented by replacing the modulus ofthis propagated wave front with that recorded without the target objectin the measurement plane 44.

The corrected wave front is then inverse propagated back at step 45 togive:P′ _(k)(r)=

⁻¹[Ψ′_(k)(u)]  11

An update step 46 makes use of an update function U2 which is:

$\begin{matrix}{{P_{k + 1}(r)} = {{P_{k}(r)} + {\beta\frac{O_{k}^{*}\left( {r - R} \right)}{{{O_{k}\left( {r - R} \right)}}_{\max}^{2}}\left( {{P_{k}^{\prime}(r)} - {\psi_{k}\left( {r,R} \right)}} \right)}}} & 12\end{matrix}$

The result of this update function generates the running estimate forthe probe function. The parameter β governs the rate of change of theprobe guess. This value should be adjusted between 0 and 2 as highervalues may lead to instability in the updated probe guess. The runningguess for the probe function may be used at step 35 for generating theexit wave front as well as producing the new estimate to be transformedat step 42 to update the running estimate of the probe function itselfin the next iteration.

FIG. 5 illustrates apparatus for providing image data which may be usedto construct a high-resolution image of a region of a target objectaccording to the above-described embodiment illustrated in FIGS. 1 and2. A source of radiation 50 provides illumination onto a lens 51 whichweakly focuses the radiation onto a selected region of a target 11. Theincident radiation has an incident wave function 52 and an exit wavefunction 53. This exit wave function is propagated across distance Dwhere a diffraction pattern is formed on an array of detectors 12. Thedistance D is advantageously sufficiently long so that the propagatedexit wave function 53 forms a Fourier diffraction pattern in thefar-field. The detector array provides at least one detector which candetect the intensity of radiation scattered by the target object 11. Alocating device 54 is provided which may be a micro actuator and thiscan locate the target object at one or more locations as desired withrespect to the target object. In this way radiation from source 50 maybe made incident on different locations of the upstream surface of thetarget 11.

Alternatively, in some applications it may be advantageous for thedistance D to be sufficiently small so that the propagated exit wavefunction 53 forms a Fresnel diffraction pattern on the detector array inthe near field.

A control unit 55 provides control signals to the micro actuator andalso receives intensity measurement results from each of the pixeldetectors in the detector array 12. The control unit 55 includes amicroprocessor 56 and a data store 57 together with a user interface 58which may include a user display and a user input key pad. The controlunit may be connected to a further processing device such as a laptop 59or PC for remote control. Alternatively it will be understood that thecontrol unit 55 could be provided by a laptop or PC. The control unit 55can automatically control the production of image data in real time.Alternatively a user can use the user interface 58 to select areas ofthe target object for imaging or provide further user input.

In use the source of radiation 50 illuminates the lens 51 withradiation. The target object 11 is selectively located by the actuator54 under control of the control unit 55. The radiation forms adiffraction pattern detected at respective locations by each of thedetectors in the detector array 12. Results from these detectors isinput to the control unit and may be stored in the data store 57. Ifonly one position is being used to derive image data the microprocessoruses this detected information together with program instructionsincluding information about the algorithm above-noted to derive theimage data. However if one or more further positions are required priorto finalizing the image data the control unit next issues signals to theactuator 54 which locates the specimen at another selected location. Theactuator may place the specimen at one of many different positions.After relocation a further diffraction pattern formed on the detectorarray is measured and the results stored in the control unit. As anexample the array 12 may be a CCD array of 1200×1200 pixels. If nofurther intensity measurements are required image data may at this stagebe generated by the control unit in accordance with the two newly storedsets of results using the algorithm above-noted. The raw image data maybe displayed or a high-resolution image generated from the image datamay be displayed on the user interface 1209 or remote display on a PC orother such device. Alternatively or additionally the image data itselfmay be utilised to determine characteristics associated with the targetobject (for example by data values being compared with predeterminedvalues.

The actuator can be used to move the target object out of the opticalpath to enable the diffraction pattern without target object to bemeasured. Alternatively this movement may be effected by anotheractuator (not shown) or by user interference.

According to a further embodiment of the invention, a diffuser covers apost-target aperture. The diffuser is arranged to diffuse the wavefrontfrom the target such that the radiation incident on the sample is spreadmore evenly over all diffraction angles in the measured diffractionpattern. By performing the measurements required to recover theillumination function, or probe function, with the diffuser in place,the effect of the diffuser can be automatically recovered as well. Thus,the diffuser may diffuse the wavefront from the target in an arbitraryway, and it is not necessary to know a priori the nature of thediffuser.

The presence of the diffuser leads to a reduction in the dynamic rangeof the diffraction pattern. As most detectors have limited dynamicrange, reducing the dynamic range of the diffraction pattern may allow amore faithful representation of the diffraction pattern to bedetermined. Furthermore, as the radiation incident on the sample isspread more evenly over all diffraction angles, the incident fluxrequired to provide the image data may be reduced, thereby reducing thepossibility of causing damage to the target object.

Any type of diffuser having an arbitrary transfer function may be used.As will be understood by the skilled man, the choice of diffuser willdepend on the properties of the radiation used, and the desireddiffusion effect. For example, for visible light the diffuser maycomprise a ground glass diffuser.

According to a further embodiment of the invention, a diffuser having aknown transfer function may be used in conjunction with a known probefunction. Such an arrangement allows the diffused probe function to becalculated, allowing the object function to be determined using aprecalculated probe function.

Throughout the description and claims of this specification, the words“comprise” and “contain” and variations of the words, for example“comprising” and “comprises”, means “including but not limited to”, andis not intended to (and does not) exclude other moieties, additives,components, integers or steps.

Throughout the description and claims of this specification, thesingular encompasses the plural unless the context otherwise requires.In particular, where the indefinite article is used, the specificationis to be understood as contemplating plurality as well as singularity,unless the context requires otherwise.

Features, integers, characteristics, compounds, chemical moieties orgroups described in conjunction with a particular aspect, embodiment orexample of the invention are to be understood to be applicable to anyother aspect, embodiment or example described herein unless incompatibletherewith.

The invention claimed is:
 1. A method of providing image data for constructing an image of a region of a target object, comprising the steps of: providing incident radiation from a radiation source at a target object and, via at least one detector, detecting an intensity of radiation scattered by the target object; estimating an object function indicating at least one characteristic of a region of the target object; estimating a probe function indicating at least one characteristic of the incident radiation; and providing image data via an iterative process responsive to the detected intensity of radiation scattered by the target object, wherein in said iterative process each of the object function and probe function are iteratively re-estimated step by step with a running estimate of the probe function being utilized to determine a running estimate of the object function associated with the target object.
 2. The method as claimed in claim 1, wherein the iteratively re-estimating the object function and the probe function comprises the steps of: multiplying the estimated object function by the estimated probe function to thereby provide an exit wave function; propagating the exit wave function to provide an estimate of an expected scattering pattern; and correcting at least one characteristic of said expected scattering pattern according to a detected intensity of radiation scattered by the target object.
 3. The method as claimed in claim 2, further comprising the steps of; inverse propagating a corrected expected scattering pattern to thereby provide an updated exit wave function; and updating the running estimate of the object function responsive to the updated exit wave function.
 4. The method as claimed in claim 3, wherein the object function is updated according to: ${O_{k + 1}(r)} = {{O_{k}(r)} + {\alpha\frac{P_{k}^{*}\left( {r - R} \right)}{{{P_{k}\left( {r - R} \right)}}_{\max}^{2}}\left( {{\psi_{k}^{\prime}\left( {r,R} \right)} - {\psi_{k}\left( {r,R} \right)}} \right)}}$ where O_(k)(r) is the current (kth) estimate of the object function, ψ_(k)(r, R) is the current exit wave, ψ′_(k)(r, R) is the updated exit wave whose Fourier Transform or Fresnel Transform has been corrected and P_(k)(r−R) is the current (kth) estimate of the illumination function, α is a constant whose value can be adjusted to optimize the performance of the algorithm.
 5. The method as claimed in claim 1, further comprising the steps of: propagating the estimated probe function to provide an estimate of an expected targetless scattering pattern; and correcting at least one characteristic of said expected targetless scattering pattern according to an intensity of radiation detected absent said target object.
 6. The method as claimed in claim 1, further comprising the steps of: inverse propagating a corrected expected targetless scattering pattern to thereby provide the running estimate for the probe function; and updating the running estimate of the probe function responsive to the updated probe function.
 7. The method as claimed in claim 6, wherein the probe function is updated according to: ${P_{k + 1}(r)} = {{P_{k}(r)} + {\beta\frac{O_{k}^{*}\left( {r - R} \right)}{{{O_{k}\left( {r - R} \right)}}_{\max}^{2}}\left( {{P_{k}^{\prime}(r)} - {\psi_{k}\left( {r,R} \right)}} \right)}}$ where O_(k)(r) is the current (kth) estimate of the object function, ψ_(k)(r, R) is the current exit wave, P′_(k)(r) is the updated illumination function whose Fourier Transform has been corrected using the measurement Ω_(P)(u) and P_(k)(r) is the current (kth) estimate of the illumination function, and β is a constant whose value can be adjusted to optimize the performance of the algorithm.
 8. The method as claimed in claim 7, wherein the estimated probe function is propagated to provide an estimate scattering pattern in a measurement plane of Φ_(k)(u)=

[P _(k)(r)] where the propagation operator

suitably models the propagation between the plane of the object and the measurement plane, wherein

comprises a Fourier Transform or a Fresnel Transform, Φ_(k)(u) is the propagated kth illumination function guess, whose modulus must match the recording Ω_(P)(u), and P_(k)(r) is the current (kth) estimate of the illumination function.
 9. The method as claimed in claim 8, wherein the corrected targetless scattering pattern is inversely propagated back to an object plane as P′ _(k)(r)=

⁻¹[Φ′_(k)(u)] where the propagation operator

⁻¹ suitably models the propagation between the measurement plane and the plane of the object, wherein

⁻¹ comprises an Inverse Fourier Transform or an Inverse Fresnel Transform, P′_(k)(r) is the corrected illumination function in the plane of the object and Φ′_(k)(u) is the corrected diffraction pattern whose modulus matches the recorded modulus of the illumination function.
 10. The method as claimed in claim 1, further comprising the steps of: updating the running estimate of the probe function and the running estimate of an object function simultaneously with each iteration.
 11. The method as claimed in claim 1, further comprising the steps of: detecting the intensity of radiation scattered by the target object with the incident radiation or a post target aperture at a first position with respect to the target object; re-positioning the incident radiation or post-target aperture at least one further position relative to the target object; subsequently detecting the intensity of radiation scattered by the target object with the incident radiation or post-target aperture at the at least one further position; and providing the image data responsive to the intensity of radiation detected as scattered at the first and at least one further position.
 12. The method as claimed in claim 11, further comprising the steps of: estimating the object function indicating at least one characteristic of said region of the target object; and estimating the probe function indicating at least one characteristic of incident radiation at the target object or the post-target aperture.
 13. The method as claimed in claim 1, further comprising the steps of: detecting the intensity of radiation provided absent the target object before and/or after locating a target object between the radiation source and the detector.
 14. The method as claimed in claim 1, further comprising the steps of: providing an initial estimate of the probe function as a prior modelled probe function or by providing a random approximation for the probe function.
 15. The method as claimed in claim 1, further comprising providing a diffuser arranged to diffuse radiation detected at the detector.
 16. The method as claimed in claim 1, wherein the target object is at least partially transparent to the incident radiation and detecting an intensity of radiation scattered by the target object comprises detecting an intensity of radiation transmitted by the target object.
 17. The method as claimed in claim 1, wherein the target object is at least partially reflective to the incident radiation and detecting an intensity of radiation scattered by the target object comprises detecting an intensity of radiation reflected by the target object.
 18. Apparatus for providing image data for generating an image of a region of a target object, comprising: a locating device for locating a target object at a predetermined location; a radiation source for providing incident radiation at a target object located by the locating device; at least one detector device for detecting an intensity of radiation scattered by the target object locating device for locating incident radiation or a post-target aperture at one or more locations with respect to the target object; a memory storing an object function indicating at least one characteristic of a region of the target object and a probe function indicating at least one characteristic of the incident radiation; and a processor for providing image data via an iterative process responsive to a detected intensity of radiation scattered by the target object, wherein in said iterative process the processor is configured to iteratively re-estimate each of the object function and the probe function step by step with a running estimate of the probe function being utilized to determine a running estimate of the object function associated with the target object.
 19. The apparatus as claimed in claim 18, wherein the incident radiation is substantially localized.
 20. The apparatus as claimed in claim 18, further comprising a diffuser arranged to diffuse radiation detected at the detector.
 21. The apparatus as claimed in claim 20, wherein the diffuser is located within a post target aperture.
 22. A non-transitory computer-readable data storage medium having instructions stored thereon which, when executed by a computer, perform the method as claimed in claim
 1. 